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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2014.1
- 수록면
- 639 - 654 (16page)
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초록· 키워드
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In [9], Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials VK(t) of classical links to the f{polynomials fK(A) of virtual links by using bracket polynomials.
In [4], M. Goussarov, M. Polyak and O. Viro introduced ¯nite type invariants of virtual knots. In this paper, we give a necessary condition for a virtual knot invariant to be of finite type by using t(a1,ㆍㆍㆍ,am)-sequences of virtual knots. Then we show that the higher derivatives f(n)K(a) of the f-polynomial fK(A) of a virtual knot K at any point a are not of ¯nite type unless n ≤ 1 and a = 1.
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참고문헌 (14)
참고문헌 신청
D. Bar-Natan / 1995 / On the Vassiliev knot invariant / Topology 34 : 423 ~ 427
H. Murakami / 1986 / On derivatives of the Jones polynomial / Kobe J. Math. 3 : 61 ~ 64
J. S. Birman / 1993 / Knot polynomials and Vassiliev's invariants / Invent. Math. 111 : 225 ~ 270
J. Zhu / 1998 / On Jones knot invariants and Vassiliev invariants / New Zealand J. Math. 27 : 294 ~ 299
K. Murasugi / 1996 / Knot Theory and Its Applications / Birkhauser
H. Murakami / 1986 / On derivatives of the Jones polynomial / Kobe J. Math. 3 : 61 ~ 64
J. S. Birman / 1993 / Knot polynomials and Vassiliev's invariants / Invent. Math. 111 : 225 ~ 270
J. Zhu / 1998 / On Jones knot invariants and Vassiliev invariants / New Zealand J. Math. 27 : 294 ~ 299
K. Murasugi / 1996 / Knot Theory and Its Applications / Birkhauser
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